Problem: Multiply the following complex numbers: $({1+i}) \cdot ({-3-4i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({1+i}) \cdot ({-3-4i}) = $ $ ({1} \cdot {-3}) + ({1} \cdot {-4}i) + ({1}i \cdot {-3}) + ({1}i \cdot {-4}i) $ Then simplify the terms: $ (-3) + (-4i) + (-3i) + (-4 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -3 + (-4 - 3)i - 4i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -3 + (-4 - 3)i - (-4) $ The result is simplified: $ (-3 + 4) + (-7i) = 1-7i $